Published October 8, 2025 | Version 3
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ANTI-SYNCHRONIZING BACKSTEPPING CONTROL DESIGN FOR ARNEODO CHAOTIC SYSTEM

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Description

In this paper, we derive new results for backstepping controller design for the anti-synchronization of
Arneodo chaotic system (1980). Backstepping control is a recursive procedure that combines the choice of
a Lyapunov function with the design of a feedback controller. In anti-synchronization of chaotic systems,
the states of the synchronized systems have the same absolute values, but opposite signs. First, we derive
an active backstepping controller for the anti-synchronization of identical Arneodo chaotic systems. Next,
we derive an adaptive backstepping controller for the anti-synchronization of identical Arneodo chaotic
system, when the system parameters are unknown. The anti-synchronization results for Arneodo chaotic
systems have been proved using Lyapunov stability theory. Numerical simulations have been shown to
illustrate the backstepping controllers derived in this paper for Arneodo chaotic system.

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ISSN
1839-9614

Related works

Is referenced by
Publication: 1839-9614 (ISSN)

Dates

Submitted
2025-10-08
In this paper, we derive new results for backstepping controller design for the anti-synchronization of Arneodo chaotic system (1980). Backstepping control is a recursive procedure that combines the choice of a Lyapunov function with the design of a feedback controller. In anti-synchronization of chaotic systems, the states of the synchronized systems have the same absolute values, but opposite signs. First, we derive an active backstepping controller for the anti-synchronization of identical Arneodo chaotic systems. Next, we derive an adaptive backstepping controller for the anti-synchronization of identical Arneodo chaotic system, when the system parameters are unknown. The anti-synchronization results for Arneodo chaotic systems have been proved using Lyapunov stability theory. Numerical simulations have been shown to illustrate the backstepping controllers derived in this paper for Arneodo chaotic system.

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https://wireilla.com/papers/ijbb/V3N1/3113ijbb03.pdf

References

  • [1] Alligood, K.T., Sauer, T. & Yorke, J.A. (1997) Chaos: An Introduction to Dynamical Systems, Springer Verlag, New York. [2] Lorenz, E.N. (1963) "Deterministic non-periodic flow," Journal of the Atmospheric Sciences, Vol. 20, pp 130-141. [3] Lakshmanan, M. & Murali, K. (1996) Nonlinear Oscillators: Controlling and Synchronization, World Scientific, Singapore. [4] Petrov, V., Gaspar, V., Masere, J. & Showalter, K. (1993) "Controlling chaos in the BelousovZhabotinsky reaction," Nature, Vol. 361, pp 240-243. [5] Kuramoto, Y. (1984) Chemical Oscillations, Waves and Turbulence, Springer Verlag, New York. [6] Van Wiggeren, G. & Roy, R. (1998) "Communicating with chaotic lasers," Science, Vol. 279, pp 1198-1200.